多尺度地震波传播的高阶梯度框架

中文摘要 AI 辅助

在多孔介质中模拟频变地震波传播仍然是一个重大挑战，因为经典的孔隙弹性理论通常需要大量约束性差的构成参数。我们研究了高阶梯度构成框架内的地震波传播，将其作为孔隙弹性介质的有效动态均匀化模型。所提出的公式扩展了经典的应变梯度弹性，通过引入与旋转变形相关的额外曲率贡献，允许在统一的连续介质框架内独立描述纵波和横波的频散。推导了一般频散关系及其宏观和微观速度极限，为模型引入的特征惯性长度和弹性长度尺度提供了直接的物理解释。该框架针对不同围压下致密砂岩中频变的P波和S波速度的实验室测量进行了验证。反演表明，一个共同的惯性特征长度和一个共同的应变梯度特征长度控制着两种波型，而额外的曲率特征长度仅对剪切波是必需的。与经典Biot理论的比较表明，所提出的框架仅使用少量有效构成参数即可再现观察到的实验室频散，提供了孔隙弹性波传播的简化构成描述。这些结果表明，高阶梯度弹性为模拟频变地震波传播提供了一种物理可解释且计算高效的替代方案，在 seismic imaging、反演和天然氢储层表征方面具有潜在应用。

英文摘要

Modeling frequency-dependent seismic wave propagation in porous media remains a major challenge because classical poroelastic theories generally require a large number of poorly constrained constitutive parameters. We investigate seismic wave propagation within a higher-order gradient constitutive framework as an effective dynamic homogenization model for poroelastic media. The proposed formulation extends classical strain-gradient elasticity by incorporating an additional curvature contribution associated with rotational deformation, allowing independent descriptions of longitudinal and transverse wave dispersion within a unified continuum framework. A general dispersion relation is derived together with its macroscopic and microscopic velocity limits, providing a direct physical interpretation of the characteristic inertial and elastic length scales introduced by the model. The framework is validated against laboratory measurements of frequency-dependent P- and S-wave velocities in tight sandstones under different confining pressures. The inversion demonstrates that a common inertial characteristic length and a common strain-gradient characteristic length govern both wave types, while an additional curvature characteristic length is required only for shear waves. Comparison with classical Biot theory shows that the proposed framework reproduces the observed laboratory dispersion using only a small number of effective constitutive parameters, providing a reduced constitutive description of poroelastic wave propagation. These results suggest that higher-order gradient elasticity offers a physically interpretable and computationally efficient alternative for modeling frequency-dependent seismic wave propagation, with potential applications to seismic imaging, inversion, and natural hydrogen reservoir characterization.

发表机构

• Institut de Physique du Globe de Paris, CNRS, Université de Paris（巴黎地球物理研究所，法国国家科学研究中心，巴黎大学）

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